Vincent Lam

Moderate structural realism about space-time

This paper sets out a moderate version of metaphysical structural realism that stands in contrast to both the epistemic structural realism of Worrall and the—radical—ontic structural realism of French and Ladyman. According to moderate structural realism, objects and relations (structure) are on the same ontological footing, with the objects being characterized only by the relations in which they stand. We show how this position fares well as regards philosophical arguments, avoiding the objections against the other two versions of structural realism. In particular, we set out how this position can be applied to space-time, providing for a convincing understanding of space-time points in the standard tensor formulation of general relativity as well as in the fibre bundle formulation.

Ontic Structural Realism as a Metaphysics of Objects

In a first approach, ontic structural realism (OSR) is a realism towards physical structures in the sense of networks of concrete physical relations, without these relations being dependent on fundamental physical objects that possess an intrinsic identity as their relata. In that vein, OSR has been developed in recent years as a metaphysics of contemporary fundamental physics, mainly non-relativistic quantum mechanics (QM), relativistic quantum field theory (QFT) and the general theory of relativity (GTR). The fundamental physical features of permutation invariance in many-particles quantum theory (Muller 2009), quantum entanglement in QM (Esfeld 2004) and in QFT (Lam 2010a), gauge invariance in quantum gauge theories (Lyre 2004) as well as background independence and gauge-theoretic diffeomorphism invariance in GTR (Rickles 2006; Esfeld and Lam 2008) have all been shown to support OSR in the following sense: these fundamental physical features can with good reason be taken to suggest all the same conclusion, namely that the fundamental physical objects – whatever they are according to the theory under consideration – are parts (relata) of a physical structure in the sense of a network of concrete physical relations. These objects do not have any existence – and in particular not any identity – independently of the structure they are part of (that is, the relations they bear to each other).

The physics and metaphysics of primitive stuff

The article sets out a primitive ontology of the natural world in terms of primitive stuff—that is, stuff that has as such no physical properties at all—but that is not a bare substratum either, being individuated by metrical relations. We focus on quantum physics and employ identity-based Bohmian mechanics to illustrate this view, but point out that it applies all over physics. Properties then enter into the picture exclusively through the role that they play for the dynamics of the primitive stuff. We show that such properties can be local (classical mechanics), as well as holistic (quantum mechanics), and discuss two metaphysical options to conceive them, namely, Humeanism and modal realism in the guise of dispositionalism. 1 Introduction 2 Primitive Ontology: Primitive Stuff 3 The Physics of Matter as Primitive Stuff 4 The Humean Best System Analysis of the Dynamical Variables 5 Modal Realism about the Dynamical Variables 6 Conclusion 1 Introduction 2 Primitive Ontology: Primitive Stuff 3 The Physics of Matter as Primitive Stuff 4 The Humean Best System Analysis of the Dynamical Variables 5 Modal Realism about the Dynamical Variables 6 Conclusion

No Categorial Support for Radical Ontic Structural Realism

Radical ontic structural realism (ROSR) asserts an ontological commitment to ‘free-standing’ physical structures understood solely in terms of fundamental relations, without any recourse to relata that stand in these relations. Bain ([2013], pp.1621–35) has recently defended ROSR against the common charge of incoherence by arguing that a reformulation of fundamental physical theories in category-theoretic terms (rather than the usual set-theoretic ones) offers a coherent and precise articulation of the commitments accepted by ROSR. In this essay, we argue that category theory does not offer a more hospitable environment to ROSR than set theory. We also show that the application of category-theoretic tools to topological quantum field theory and to algebraic generalizations of general relativity do not warrant the claim that these theories describe ‘object-free’ structures. We conclude that category theory offers little if any comfort to ROSR. 1 Introduction: Ridding Structures of Objects 2 The Set-theoretic Peril for Radical Ontic Structural Realism 3 Bain’s Categorial Strategy to Save Radical Ontic Structural Realism 4 Throwing out the Relations with the Relata 5 Categorial and Set-theoretical Structures 6 Radical Suggestions from Topological Quantum Field Theory? 7 Sheaves of Einstein Algebras as Radical Structures? 8 Conclusions 1 Introduction: Ridding Structures of Objects 2 The Set-theoretic Peril for Radical Ontic Structural Realism 3 Bain’s Categorial Strategy to Save Radical Ontic Structural Realism 4 Throwing out the Relations with the Relata 5 Categorial and Set-theoretical Structures 6 Radical Suggestions from Topological Quantum Field Theory? 7 Sheaves of Einstein Algebras as Radical Structures? 8 Conclusions

Gravitational and Nongravitational Energy: The Need for Background Structures

The aim of this article is to discuss some aspects of the nature of gravitational energy within the general theory of relativity. Some aspects of the difficulties to ascribe the usual features of localization and conservation to gravitational energy are reviewed and considered in the light of the dual role of the dynamical gravitational field, which encodes both inertio-gravitational effects and the chronogeometrical structures of space-time. These considerations will lead us to discuss the fact that the very notion of energy—gravitational or not—is actually well defined in the theory only with respect to some background structure.

The Entanglement Structure of Quantum Field Systems

This article discusses the peculiar features of quantum entanglement and quantum non-locality within the algebraic approach to relativistic quantum field theory (RQFT). The debate on the ontology of RQFT is considered in the light of these well-known but little discussed features. In particular, this article examines the ontic structural realist understanding of quantum entanglement and quantum non-locality and its contribution to this debate.

The Singular Nature of Spacetime

We consider to what extent the fundamental question of spacetime singularities is relevant for the philosophical debate about the nature of spacetime. After reviewing some basic aspects of the spacetime singularities within general relativity, we argue that the well known difficulty to localize them in a meaningful way may challenge the received metaphysical view of spacetime as a set of points possessing some intrinsic properties together with some spatiotemporal relations. Considering the algebraic formulation of general relativity, we argue that the spacetime singularities highlight the philosophically misleading dependence on the standard geometric representation of spacetime.

Quantum structure and spacetime

The aim of this paper is twofold. In the first part, it clarifies the nature of wave function within the framework of the primitive ontology approach to quantum mechanics using the tools of ontic structural realism. In the second part, it critically discusses the primitive ontological move of postulating from the start matter localized in spacetime as the ultimate referent for quantum theory, in particular the case where the latter is applied to the general relativistic gravitational field.

Chapter 6 Structural Aspects of Space-Time Singularities

Abstract We investigate the possible relevance of space-time singularities (within the theory of general relativity) for the debate about the nature of space-time. Standard attempts to describe space-time singularities in terms of local entities and local properties are discussed. It seems that space-time singularities possess some non-local or global aspects in the sense that they violate some basic aspects of (pre-)locality, which are inherent in the standard differential geometric representation of space-time. These possible non-local or global aspects of space-time underline the fact that the debate about the nature of space-time should not focus only on local aspects of space-time (such as space-time points) and should not be too dependent on one specific mathematical representation. In particular, we briefly discuss the possible relevance of the algebraic formulation of the theory of general relativity for the ‘problem’ of space-time singularities. Based on these considerations, a structural realist interpretation of space-time is proposed.